Fluorescence diffusion physics problem

In summary, we consider a simple model where a cell is illuminated with a bleaching pulse of light in a pattern of parallel planes. At time t=0, the remaining fluorescence intensity is given by Θ(x)= C(i) + C(1)sin(2pix/L), where C(0) is greater than C(1) and L is the periodicity of the bleach pattern. The mean fluorescence intensity immediately after bleaching is equal to C(0), and at later times, the fluorescence intensity is Θ(x)= C(0) + Δ(t)sin(2pix/L). Using the 1D diffusion equation, we can derive an expression for the diffusion constant D in terms of the measured quantity Δ(t
  • #1
cwraabe
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0

Homework Statement


As a simple model, suppose you arrange for the intense bleaching pulse of light to illuminate
a cell in a pattern of parallel planes. That is, immediately after bleaching (at time t=0), the
remaining fluorescence intensity Θ(x) has the form Θ(x)= C(i) + C(1)sin(2pix/L) where the two C terms are constants with C(0) greater than C(1). The constant L is the periodicity of the bleach pattern. A. Show that the mean fluorescence intensity immediately after bleaching equals C(0). B. At later times, the fluorescence intensity has the form Θ(x)= C(0) + Δ(t)sin(2pix/L). Derive an expression for the diffusion constant D of the fluorescent molecules in terms of the measured quantity Δ(t). Assume that the region of interest is sufficiently small that you can approximate the cell as having infinite volume.


Homework Equations

1D diffusion equation perhaps?



The Attempt at a Solution

obeys the 1D diffusion equation as the instructor told us this.
We only need to calculate within 1 period, from 0 to L.

 
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  • #2
A. The mean fluorescence intensity is found by integrating Θ(x), thus the mean intensity is C(0). B. We start with the 1D diffusion equation: ∂Θ/∂t = D∂2Θ/∂x2. Integrating over one period, we have ∫0L∂Θ/∂t dx = D∫0L∂2Θ/∂x2dx. At t=0, Θ(x)=C(0)+C(1)sin(2pix/L), so when we integrate, we get ∫0L∂Θ/∂t dx = 0. On the right side, we use integration by parts and get D∫0L∂2Θ/∂x2dx = -D[Θ(L)-Θ(0)] = -DC(1). Thus, ∂Θ/∂t = -DC(1)/L. Since we know that at later times, Θ(x)=C(0)+Δ(t)sin(2pix/L), we can substitute this into the equation to obtain ∂Θ/∂t = -D(C(0)+Δ(t))/L. Solving for the diffusion constant, we get D = -L∂Θ/∂t/(C(0)+Δ(t)).
 

Related to Fluorescence diffusion physics problem

1. What is fluorescence diffusion?

Fluorescence diffusion is the process by which fluorescent particles or molecules move within a medium or solution due to random thermal motion. This movement is caused by collisions between the particles and molecules, and it can be described by diffusion equations.

2. How does fluorescence diffusion affect fluorescence imaging?

Fluorescence diffusion can affect fluorescence imaging by causing blurring or spreading of the fluorescent signal. This can make it more difficult to accurately measure the location and intensity of fluorescence, especially in complex or crowded environments.

3. What factors influence the rate of fluorescence diffusion?

The rate of fluorescence diffusion can be influenced by several factors, including the size and shape of the fluorescent particles or molecules, the viscosity of the medium or solution, and the temperature. Additionally, the presence of other molecules in the medium can also affect the rate of diffusion.

4. How is fluorescence diffusion related to Brownian motion?

Brownian motion is a type of random motion exhibited by particles in a fluid due to collisions with the surrounding molecules. Fluorescence diffusion is also caused by the random thermal motion of particles, and it can be described by similar equations as those used to describe Brownian motion.

5. What techniques are used to study fluorescence diffusion?

There are several techniques used to study fluorescence diffusion, including fluorescence correlation spectroscopy, fluorescence recovery after photobleaching, and single-particle tracking. These techniques allow researchers to measure the diffusion coefficient and other parameters related to fluorescence diffusion in different systems.

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